Glad that you have a job,even if it's and intern with only a stipend. You, in fact have a good practical chance at hand to prove yourself and get the job that's promised. In many fields, this is a chance for the employer and the employee to get acquainted better and decide on the suitability, remuneration etc.
Please study the company, its products, its clients,the company's website, how it can be improved,web portal, integrity of the systems,site protocols and drafts,checking databases,marketing plans,analyzing trends and contents of the client's requirements etc. Choose a few avenues that are your strengths and focus on assessing the shortcomings and areas of improvement.
Once you are in the intern program, in the beginning try to blend in the team rather than trying to be smart and pointing out faults or giving opinions without being asked. Once the people around you 'accept' you as a colleague, then you can start contributing your inputs on the areas that you think you can make a difference. Any job that comes your way, do it diligently to prove that you are the right candidate for the permanent job. Don't hesitate to shadow or tag along with one or two good senior employees who are good at teaching practical tips. In a month or two you would be comfortable.
Nothing is assured in terms of promotions 6 months down the line but if you are sincere in your efforts to work and have the keeness and aptitude to learn I'm sure the company would promote you. While you are there, please gradually cultivate your contacts as thye would be resourceful in the future at the same company or in your search for a better job. If by chance they don't promote you don't be disheartened, you will have a certificate of expereince as an intern, our stipend, some references.
It's worth refresh what makes a good web analyst.The key focus areas would be your skills or proficiency in data visualization, problem solving, communication, adaptation and technical areas. Have a grasp of traffic drivers and how you can improve traffic pathways etc. All the best.